Floating-point exponential functions for DSP-enabled FPGAs

This article presents a generator of floating-point exponential operators targeting recent FPGAs with embedded memories and DSP blocks. A single-precision operator consumes just one DSP block, 18 Kbits of dual-port memory, and 392 slices on Virtex-4. For larger precisions, a generic approach based on polynomial approximation is used and proves more resource-efficient than the literature. For instance a double-precision operator consumes 5 BlockRAM and 12 DSP48 blocks on Virtex-5, or 10 M9k and 22 18 × 18 multipliers on Stratix III. This approach is flexible and is demonstrated to scale up to quadruple-precision, while enabling frequencies close to the FPGA´s nominal frequency. All the proposed architectures are last-bit accurate for all the floating-point range. They are available in the open-source FloPoCo framework.